My girlfriend is overly affectionate and doesn't understand Personal space?

she's always touching me in some way or another. It's not necessarily sexual. She seems to want to walk together holding hands or my bicep/elbow. Which is fine when it's moderate.
I just keep thinking in my head fuck off but if I bring it up it will make things weird. I think she's territorial but at the same time tries to 'show' everyone where cute or some shit.

Another thing is she doesn't take into account the environment. If I'm with my friends she will come over and sit on my lap. But why? If there's other seats. It's gotten to the point where my mates have noticed and they start laughing when she's walking towards us.
I know this sounds like I dislike her but I don't where 2 months in and first yr of uni.
I have a problem because I don't want to reject her excessive affection in front of others.
Is there a nice way of getting the message across?
My girlfriend is overly affectionate and doesn't understand Personal space?
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